On Connectivity Thresholds in the Intersection of Random Key Graphs on Random Geometric Graphs

Abstract

In a random key graph (RKG) of $n$ nodes each node is randomly assigned a key ring of $K_n$ cryptographic keys from a pool of $P_n$ keys. Two nodes can communicate directly if they have at least one common key in their key rings. We assume that the $n$ nodes are distributed uniformly in $[0,1{]}^2.$ In addition to the common key requirement, we require two nodes to also be within $r_n$ of each other to be able to have a direct edge. Thus we have a random graph in which the RKG is superposed on the familiar random geometric graph (RGG). For such a random graph, we obtain tight bounds on the relation between $K_n,$ $P_n$ and $r_n$ for the graph to be asymptotically almost surely connected.

Accepted for Publication at ISIT 2013. 5 Pages (main text) + 6 pages (appendix)

References in corpus (1)

• Zero-one laws for connectivity in random key graphs